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if x+ y+ z =pie...........and tan x *tan z=2 as well as tan y *tan z = 18 ,then (tan z )^2 is equal to what ?
The answer is 16.
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1 solution
tan(x + (y + z)) = [tan(x) + tan(y + z)] / [1 - tan(x)*tan(y + z)] = 0 since x + y + z = pi.
So tan(x) + tan(y + z) = 0 ----> -tan(x) = [tan(y) + tan(z)] / [1 - tan(y)*tan(z)].
Now 1 - tan(y) tan(z) = 1 - 18 = -17, so we have 17 tan(x) = tan(y) + tan(z).
Multiply through by tan(z) to get 17 tan(x) tan(z) = tan(y)*tan(z) + tan^2(z),
and so 17 * 2 = 18 + tan^2(z) -----> tan^2(z) = 16.